If Black -Scholes model shares common intuition with risk-neutral option pricing model (also known as the binomial option pricing model).

If Black -Scholes model shares common intuition with risk-neutral option pricing model (also known as the binomial option pricing model). One of the biggest underlying assumptions of risk-neutral (binomial) model is that we live in a risk-neutral world. In a risk-neurtal world, all investors only demand risk-free return on all asset. Although he risk-neutral assumption is counterfactual, it is brilliant and desirable because the prices of an option estimated by risk-neutral approach are exactly the same with or without the risk-neutral assumption. So why is that the case and how is risk-neutral assumption greatly simplifies the calculations of risk neutral option pricing approach?